SIAM Journal on Scientific Computing, Volume 42, Issue 5, Page B1173-B1192, January 2020.
We propose a new numerical method to solve the linearized problem of the travel time tomography with incomplete data. Our method is based on the technique of the truncation of the Fourier series with respect to a special basis of $L^{2}$. This way we derive a boundary value problem for a system of coupled PDEs of the first order. This problem is solved by the quasi-reversibility method. The spatially dependent Fourier coefficients of the solution to the linearized eikonal equation are obtained this way. Numerical results for highly noisy data are presented.

中文翻译：

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数据不完整的线性旅行时间层析成像问题的数值解

SIAM科学计算杂志，第42卷，第5期，第B1173-B1192页，2020年1月。
我们提出了一种新的数值方法，用于解决数据不完整的行进时间层析成像的线性化问题。我们的方法基于关于$ L ^ {2} $的特殊基础的傅里叶级数截断技术。这样，我们导出一阶耦合PDE系统的边值问题。该问题通过准可逆性方法解决。用这种方法获得线性化方程方程解的与空间有关的傅立叶系数。给出了高噪声数据的数值结果。